A body of mass $40\,kg$ resting on rough horizontal surface is subjected to a force $P$ which is just enough to start the motion of the body. If $\mu_{ s }=5, \mu_{ x }=0.4$, $g =10\,m / s ^2$ and the force $P$ is continuously applied on the body, then the acceleration of the body is $.........m/s^{2}$
AIIMS 2015, Difficult
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(b)
Since $P$ is the force which is just enough to start the motion of the body,
$P =\mu_{ s } N =\mu_{ s }\,mg$
When the body moves under this force, the net force on body is given by
$F=m a=P-f$
$\Rightarrow ma =\mu_{ s } mg -\mu_{ k } N$
$= m \left(\mu_{ s }-\mu_{ k }\right) g$
$\Rightarrow a =\left(\mu_{ s }-\mu_{ k }\right) g$
$=(0.5-0.4)(10)\,m / s ^2$
$\Rightarrow a =1\,m / s ^2$
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